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Partition of graphs with maximum degree ratio

Valentin Bouquet 1 François Delbot 2 Christophe Picouleau 1
1 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
CEDRIC - Centre d'études et de recherche en informatique et communications
Abstract : Given a graph and a non trivial partition (V1,V2) of its vertices, the satisfaction of a vertex v of Vi, i=1,2 is the ratio between the size of its closed neighborhood in Vi and the total size of its closed neighborhood. The worst ratio over all the vertices defines the quality of the partition. We define q(G) the degree ratio of a graph as the maximum of the worst ratio over all the non trivial partitions. We give bounds and exact values of q(G) for some classes of graphs. We also show some complexity results.
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https://hal.archives-ouvertes.fr/hal-02907108
Contributor : Christophe Picouleau <>
Submitted on : Monday, July 27, 2020 - 10:56:13 AM
Last modification on : Tuesday, March 23, 2021 - 9:28:02 AM

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  • HAL Id : hal-02907108, version 1
  • ARXIV : 2007.12434

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Valentin Bouquet, François Delbot, Christophe Picouleau. Partition of graphs with maximum degree ratio. 2020. ⟨hal-02907108⟩

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